STA 210 Lecture Notes - Lecture 5: Simple Random Sample
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~ Statistics Lecture #5 ~
Introduction to Sampling and Confidence Intervals
o Preview: Statistical Sampling
o The goal is to make inferences about a big group of individuals or items, from what we
know about from a well-chosen sample group.
o Specifically to estimate a number we don’t know in that larger group, with one we do know
from the sample
o Be able to quantify the confidence you can have in those inferences.
o We have to understand this can only be done probabilistically.
o An Example
o We have 132 students currently enrolled in this class.
o Canvas tells us various things about students’ activity so we can see who is engaged and who
o Suppose we want to estimate the proportion of the class with over 100 “Page Views.”
o We might do that based on a sample of 30 students.
o Sensible Estimate?
o Statistical science is about how to mathematically quantify the goodness of this common
o How the sample is taken is critical to that process.
o Statistical Sampling is More than Common Sense
o It is a probabilistic endeavor.
o It tells us a lot about how sample statistics behave from sample to sample.
o Provided we know that the sample was taken probabilistically
o Language in Upcoming Reading
o Population: Larger collection of subjects/items that you are interested in understanding
o Sample: Subject/items chosen to be measured or interviewed
▪ Chosen from population
o List of Individuals:
o Population Parameter: Number the describes the population
▪ E.g. true proportion of all UK students who would answer “yes”
o Sample Statistic: Number that describes the sample
▪ E.g. observed proportion in sample who answered “yes”
o Simple Random Sampling: A Non-Trivial Probabilistic Idea
o A simple random sample (SRS) of size n consists of n individuals chosen from the
population in such a way that every set of n individuals had the same chance of being chosen.
▪ Notice this did not say “a kinda unbiased sort of thing that we made sure was spread
out and representative and stuff like that. You know, random.”
• Much more precise than that.
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